Scilab Function
Last update : 12/1/2004

arsimul - armax simulation

### Calling Sequence

  `[z]=arsimul(a,b,d,sig,u,[up,yp,ep])`
  `[z]=arsimul(ar,u,[up,yp,ep])`

### Parameters

- `ar`: an armax process. See armac.
- `a`: is the matrix[Id,a1,...,a_r] of dimension (n,(r+1)*n)
- `b`: is the matrix[b0,......,b_s] of dimension (n,(s+1)*m)
- `d`: is the matrix[Id,d_1,......,d_t] of dimension (n,(t+1)*n)
- `u`: is a matrix (m,N), which gives the entry u(:,j)=u_j
- `sig`: is a (n,n) matrix e_{k} is an n-dimensional Gaussian process with variance I
- `up, yp`: optional parameter which describe the past. up=[ u_0,u_{-1},...,u_{s-1}]; yp=[ y_0,y_{-1},...,y_{r-1}]; ep=[ e_0,e_{-1},...,e_{r-1}]; if they are omitted, the past value are supposed to be zero
- `z`: z=[ y(1),....,y(N)]

### Description

simulation of an n-dimensional armax process A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)

A(z)= Id+a1*z+...+a_r*z^r; ( r=0 => A(z)=Id) B(z)= b0+b1*z+...+b_s z^s; ( s=-1 => B(z)=[]) D(z)= Id+d1*z+...+d_t z^t; ( t=0 => D(z)=Id) z et e are in R^n et u in R^m

### Method

a state-space representation is constructed and ode with the option "discr" is used to compute z

### Author

J-Ph.C.;